Resolving Ambiguity |
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Geometry Expressions uses your drawing to resolve ambiguities. For example, the following drawing shows two triangles, ABC and ADC. Both have two sides of constrained length, one of length a and the other of length b, as well as an angle θ, an unincluded angle: ![]() Two sides and the included angle uniquely define a triangle, but two sides and an unincluded angle do not. So if you specify a triangle using two sides and an unincluded angle, it’s not unique: two possible solutions exist. In the drawing above, it could be either ABC or ADC. In ambiguous cases like this, Geometry Expressions determines which solution you intend according to how you drew the objects. Both triangles have one included angle(BAC and DAC), one unincluded yet constrained angle(ACB and ACD), and an unconstrained and unincluded angle(ABC and ADC). The key difference between the two triangles is whether this last angle is acute or obtuse. So the application consults your drawing to see how you drew this key angle. If you drew it as acute, the application constructs the triangle ABC; if you drew it as obtuse, it constructs ADC instead. A trapezoid with the constraints specified below also has two possible solutions for the angle ABC — one convex, the other concave. Because the drawing is convex, Geometry Expressions chooses the convex solution: ![]() |